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Fractal dimensions of in vitro tumor cell proliferation.

Lambrou GI, Zaravinos A - J Oncol (2015)

Bottom Line: Our results show that the temporal transitions from one state to the other also follow nonlinear dynamics.Such systems biology approaches are very useful in understanding the nature of cellular proliferation and growth.From a clinical point of view, our results may be applicable not only to primary tumors but also to tumor metastases.

View Article: PubMed Central - PubMed

Affiliation: 1st Department of Pediatrics, University of Athens, Choremeio Research Laboratory, Thivon & Levadeias, 11527 Athens, Greece.

ABSTRACT
Biological systems are characterized by their potential for dynamic adaptation. One of the challenges for systems biology approaches is their contribution towards the understanding of the dynamics of a growing cell population. Conceptualizing these dynamics in tumor models could help us understand the steps leading to the initiation of the disease and its progression. In vitro models are useful in answering this question by providing information over the spatiotemporal nature of such dynamics. In the present work, we used physical quantities such as growth rate, velocity, and acceleration for the cellular proliferation and identified the fractal structures in tumor cell proliferation dynamics. We provide evidence that the rate of cellular proliferation is of nonlinear nature and exhibits oscillatory behavior. We also calculated the fractal dimensions of our cellular system. Our results show that the temporal transitions from one state to the other also follow nonlinear dynamics. Furthermore, we calculated self-similarity in cellular proliferation, providing the basis for further investigation in this topic. Such systems biology approaches are very useful in understanding the nature of cellular proliferation and growth. From a clinical point of view, our results may be applicable not only to primary tumors but also to tumor metastases.

No MeSH data available.


Related in: MedlinePlus

Graphical representation of self-similarity calculations for the 1321N1 cells with respect to rate of proliferation (a), for the A172 cells with respect to rate of proliferation (b), for the TE671 cells with respect to the rate of proliferation (c), for the A172 cells with respect to the velocity of cell growth (d), for the CCRFCEM cells with respect to the rate of proliferation (e), and for the A172 cells with respect to the acceleration of cell growth.
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fig9: Graphical representation of self-similarity calculations for the 1321N1 cells with respect to rate of proliferation (a), for the A172 cells with respect to rate of proliferation (b), for the TE671 cells with respect to the rate of proliferation (c), for the A172 cells with respect to the velocity of cell growth (d), for the CCRFCEM cells with respect to the rate of proliferation (e), and for the A172 cells with respect to the acceleration of cell growth.

Mentions: We measured the proliferation of the three CNS tumor cells and the CCRF-CEM cells in vitro. Due to the large amount of data, the proliferation results are presented in three-dimensional graphs. The time-series proliferation results in the A172, 1321N1, and TE671 cells revealed that proliferation follows an oscillatory pattern (Figures 1–3). The rate of growth [N(t + 1)/Nt] appeared to manifest the most stable oscillatory pattern, among all measurements that we performed (Figures 1(b), 2(b), and 3(b)). In order to resolve more the patterns of oscillation, we present the proliferative pattern for the CCRF-CEM cells, which resembles that of adherent cells (Figure 4). As a representative resolution, the proliferation dynamics of the A172 cells (Figure 5), characteristic for all adherent cell lines, clearly revealed an oscillatory pattern in cellular growth velocity (Figure 6) and acceleration (Figure 7), respectively. It appears that cells do not proliferate in a linear pattern; rather they oscillate while adapting to the environmental conditions. Apart from testing this in adherent cells, we also applied our question to cells growing in suspension. Of major interest, these cells also exhibited similar dynamics (Figure 8). Therefore, our results support that different cell types manifest similar proliferation patterns, suggesting that a similar self-similarity pattern exists among different cellular types. In order to investigate self-similarity, it was necessary to show that cell proliferation factors follow some form of repetition. In systems biology, when the first derivative dln⁡N/dln⁡R remains constant in a space R, it is a hint of self-similarity. Interestingly, the rate of proliferation was equal to 1 for all cell types, while for the growth velocity and acceleration for the A172 cells it was equal to 0.80888 (Figure 9). In order to conceive the meaning of those numbers, two shapes with the same self-similarity measures are mentioned: the Cantor sets (dln⁡N/dln⁡R = 1) and the Apollonian Gasket (self-similarity value = 0.8). Our results confirmed two interesting points: (1) cell growth factors follow oscillatory dynamics (of nonlinear nature) and (2) different cell types followed similar dynamics of growth, irrespective of whether they grow as adherent or suspension cells, hinting towards a common mechanism of cellular proliferation.


Fractal dimensions of in vitro tumor cell proliferation.

Lambrou GI, Zaravinos A - J Oncol (2015)

Graphical representation of self-similarity calculations for the 1321N1 cells with respect to rate of proliferation (a), for the A172 cells with respect to rate of proliferation (b), for the TE671 cells with respect to the rate of proliferation (c), for the A172 cells with respect to the velocity of cell growth (d), for the CCRFCEM cells with respect to the rate of proliferation (e), and for the A172 cells with respect to the acceleration of cell growth.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4389830&req=5

fig9: Graphical representation of self-similarity calculations for the 1321N1 cells with respect to rate of proliferation (a), for the A172 cells with respect to rate of proliferation (b), for the TE671 cells with respect to the rate of proliferation (c), for the A172 cells with respect to the velocity of cell growth (d), for the CCRFCEM cells with respect to the rate of proliferation (e), and for the A172 cells with respect to the acceleration of cell growth.
Mentions: We measured the proliferation of the three CNS tumor cells and the CCRF-CEM cells in vitro. Due to the large amount of data, the proliferation results are presented in three-dimensional graphs. The time-series proliferation results in the A172, 1321N1, and TE671 cells revealed that proliferation follows an oscillatory pattern (Figures 1–3). The rate of growth [N(t + 1)/Nt] appeared to manifest the most stable oscillatory pattern, among all measurements that we performed (Figures 1(b), 2(b), and 3(b)). In order to resolve more the patterns of oscillation, we present the proliferative pattern for the CCRF-CEM cells, which resembles that of adherent cells (Figure 4). As a representative resolution, the proliferation dynamics of the A172 cells (Figure 5), characteristic for all adherent cell lines, clearly revealed an oscillatory pattern in cellular growth velocity (Figure 6) and acceleration (Figure 7), respectively. It appears that cells do not proliferate in a linear pattern; rather they oscillate while adapting to the environmental conditions. Apart from testing this in adherent cells, we also applied our question to cells growing in suspension. Of major interest, these cells also exhibited similar dynamics (Figure 8). Therefore, our results support that different cell types manifest similar proliferation patterns, suggesting that a similar self-similarity pattern exists among different cellular types. In order to investigate self-similarity, it was necessary to show that cell proliferation factors follow some form of repetition. In systems biology, when the first derivative dln⁡N/dln⁡R remains constant in a space R, it is a hint of self-similarity. Interestingly, the rate of proliferation was equal to 1 for all cell types, while for the growth velocity and acceleration for the A172 cells it was equal to 0.80888 (Figure 9). In order to conceive the meaning of those numbers, two shapes with the same self-similarity measures are mentioned: the Cantor sets (dln⁡N/dln⁡R = 1) and the Apollonian Gasket (self-similarity value = 0.8). Our results confirmed two interesting points: (1) cell growth factors follow oscillatory dynamics (of nonlinear nature) and (2) different cell types followed similar dynamics of growth, irrespective of whether they grow as adherent or suspension cells, hinting towards a common mechanism of cellular proliferation.

Bottom Line: Our results show that the temporal transitions from one state to the other also follow nonlinear dynamics.Such systems biology approaches are very useful in understanding the nature of cellular proliferation and growth.From a clinical point of view, our results may be applicable not only to primary tumors but also to tumor metastases.

View Article: PubMed Central - PubMed

Affiliation: 1st Department of Pediatrics, University of Athens, Choremeio Research Laboratory, Thivon & Levadeias, 11527 Athens, Greece.

ABSTRACT
Biological systems are characterized by their potential for dynamic adaptation. One of the challenges for systems biology approaches is their contribution towards the understanding of the dynamics of a growing cell population. Conceptualizing these dynamics in tumor models could help us understand the steps leading to the initiation of the disease and its progression. In vitro models are useful in answering this question by providing information over the spatiotemporal nature of such dynamics. In the present work, we used physical quantities such as growth rate, velocity, and acceleration for the cellular proliferation and identified the fractal structures in tumor cell proliferation dynamics. We provide evidence that the rate of cellular proliferation is of nonlinear nature and exhibits oscillatory behavior. We also calculated the fractal dimensions of our cellular system. Our results show that the temporal transitions from one state to the other also follow nonlinear dynamics. Furthermore, we calculated self-similarity in cellular proliferation, providing the basis for further investigation in this topic. Such systems biology approaches are very useful in understanding the nature of cellular proliferation and growth. From a clinical point of view, our results may be applicable not only to primary tumors but also to tumor metastases.

No MeSH data available.


Related in: MedlinePlus